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Amyloid-β peptide dimers undergo a random coilto β-sheet transition in the aqueous phase but notat the neuronal membraneHebah Fataftaa , Mohammed Khaleda , Michael C. Owenb,c , Abdallah Sayyed-Ahmadd , and Birgit Strodela,e,1

aInstitute of Biological Information Processing (IBI-7: Structural Biochemistry), Forschungszentrum Julich, 52425 Julich, Germany; bCentral EuropeanInstitute of Technology, Masaryk University, Brno 625 00, Czech Republic; cInstitute of Chemistry, University of Miskolc, 3515 Miskolc-Egyetemvaros,Hungary; dDepartment of Physics, Birzeit University, 71939 Birzeit, Palestine; and eInstitute of Theoretical and Computational Chemistry, Heinrich HeineUniversity Dusseldorf, 40225 Dusseldorf, Germany

Edited by Gerhard Hummer, Max Planck Institute for Biophysics, Frankfurt am Main, Germany, and accepted by Editorial Board Member Angela M.Gronenborn August 16, 2021 (received for review March 31, 2021)

Mounting evidence suggests that the neuronal cell membrane isthe main site of oligomer-mediated neuronal toxicity of amyloid-βpeptides in Alzheimer’s disease. To gain a detailed understandingof the mutual interference of amyloid-β oligomers and the neu-ronal membrane, we carried out microseconds of all-atom molec-ular dynamics (MD) simulations on the dimerization of amyloid-β(Aβ)42 in the aqueous phase and in the presence of a lipid bilayermimicking the in vivo composition of neuronal membranes. Thedimerization in solution is characterized by a random coil to β-sheet transition that seems on pathway to amyloid aggregation,while the interactions with the neuronal membrane decrease theorder of the Aβ42 dimer by attenuating its propensity to form aβ-sheet structure. The main lipid interaction partners of Aβ42 arethe surface-exposed sugar groups of the gangliosides GM1. As theneurotoxic activity of amyloid oligomers increases with oligomerorder, these results suggest that GM1 is neuroprotective againstAβ-mediated toxicity.

Alzheimer’s disease | amyloid-β | neuronal membrane | moleculardynamics | transition network

In Alzheimer’s disease (AD), amyloid-β peptide (Aβ) aggre-gates into fibrils and subsequently accumulates as plaques

within the neural tissue (1). An increasing number of studiessuggest that the smaller soluble oligomers formed in the ear-lier stages of the aggregation process are the main cytotoxicspecies affecting the severity and progression of AD (2–4). Aβdimers have been reported to be the smallest toxic oligomer thataffects synaptic plasticity and impairs memory (5, 6). Therefore,a detailed characterization of Aβ dimerization is an essentialstep toward developing a better understanding of the aggrega-tion process. However, its transient nature (resulting from itshigh aggregation tendency), its plasticity, and its equilibriumwith both the monomer and higher-order oligomers all makethe Aβ dimer extremely challenging to study experimentally. Infact, a large amount of the experimental studies performed onAβ dimers employ some kind of cross-linking to stabilize them(7–9). On the other hand, covalently cross-linked Aβ dimersare certainly of biological relevance, as such species have beenretrieved from the brains of AD patients and their neurotox-icity has been demonstrated (6, 10). Apart from this, recenttechnological developments, such as advanced single-moleculefluorescence spectroscopy and imaging, opened the way to char-acterize amyloid oligomers without the need to stabilize them bycross-linking (11, 12). Molecular dynamics (MD) simulations arealso able to provide atomic insight into the temporal evolutionof the dimer structure without the need of cross-linking (13, 14).Previous simulations of Aβ dimers were modeled in the aque-ous phase only, and thus they lacked essential details from thecellular context. Consideration of the latter is particularly impor-tant if one wishes to reveal the mechanism of toxicity that has

been shown to rely on direct contact with the lipid membrane ofneurons by Aβ oligomers (15, 16).

Many studies have been done to understand the conse-quences of Aβ–membrane interactions; however, it is extremelydifficult to capture these transient interactions with experi-mental methods. This becomes possible with MD simulationsand this problem is addressed in the current work. We usean aggregate of 24 µs of MD simulations to investigate thedimerization of the full-length Aβ42 peptide both in solu-tion and in the presence of a model lipid bilayer includ-ing six lipid types to mimic the composition of a neuronalcell membrane (17–19): 38% 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 24% 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine (POPE), 5% 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-L-serine (POPS), 20% cholesterol (CHOL),9% sphingomyelin (SM), and 4% monosialotetrahexosylgan-glioside (GM1) (Fig. 1A). For modeling Aβ we employCharmm36m, a force field adjusted for intrinsically disorderedproteins (IDPs), to model their preference to adopt extendedstructures. When applied to monomeric Aβ, Charmm36m yieldsmore than 80% of the structures in a random coil and extended

Significance

The aggregation of the amyloid-β peptide (Aβ) into neuro-toxic oligomers is central to the development of Alzheimer’sdisease. One possible source of their toxicity results frominteractions of the Aβ oligomers with the neuronal mem-brane, damaging membrane integrity and thus neurons.However, molecular details of these interactions are unclear.Here, we contrast the dimerization of Aβ in solution andat the neuronal membrane. Our results clearly indicatethat the sugar moieties of GM1 sequester Aβ by form-ing key hydrogen bonds with the peptide, which divertsthe configuration of the Aβ dimers away from damagingβ-sheet–rich structures. These findings underline the impor-tance of GM1 in Alzheimer’s disease progression and pro-vide a nanoscopic basis for its reported neuroprotectiveeffect.

Author contributions: H.F., M.C.O., and B.S. designed research; H.F., M.K., and M.C.O.performed research; H.F., M.K., and M.C.O. analyzed data; H.F., A.S.-A., and B.S. wrotethe paper; and A.S.-A. and B.S. supervised the work.y

The authors declare no competing interest.y

This article is a PNAS Direct Submission. G.H. is a guest editor invited by the EditorialBoard.y

This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).y1 To whom correspondence may be addressed. Email: b.strodel@fz-juelich.de.y

This article contains supporting information online at https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.2106210118/-/DCSupplemental.y

Published September 20, 2021.

PNAS 2021 Vol. 118 No. 39 e2106210118 https://doi.org/10.1073/pnas.2106210118 | 1 of 10

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Fig. 1. (A) A snapshot of the neuronal membrane containing 38% POPC,24% POPE, 5% POPS (collectively shown as gray surface with their phospho-rous atoms indicated by gray spheres), 20% CHOL (red sticks), 9% SM (greenspheres), and 4% GM1 (yellow spheres). In the following, PC, PE, and PS aresynonymously used for POPC, POPE, and POPS, respectively. (B and C) Radialdistribution functions for (B) lipid pairings of identical type and (C) lipid–CHOL pairings. The P atoms of PC, PE, PS, and SM and the O atoms of CHOLand GM1 were used as reference atoms for the RDF calculations. The RDFsare averaged over both membrane leaflets. The x axis shows the distancesbetween the respective atom pairs. Since CHOL resides deeper inside themembrane, it is possible that the O atom of CHOL and the reference atomsof the other lipids are above each other, explaining why not all of the RDFsapproach zero for x = 0. The colors of the functions refer to the lipids asindicated in the color key in B. Pairs with RDF > 1 are considered to formclusters.

state, and the remaining ones feature transient β-hairpins, whichis in acceptable agreement with experimental data (20). More-over, Charmm36m outperforms other force fields when it comesto modeling peptide aggregation (21, 22). To the best of ourknowledge, this simulation study breaks ground on two fronts:1) It exceeds the simulation time of previous studies modelingAβ–membrane interactions by an order of magnitude, and 2)it studies the aggregation of Aβ on a bilayer containing morethan three different lipid types. Lipid bilayers of a complexitycomparable to the one modeled here have been thus far stud-ied only at the coarse-grained level (23, 24). We also analyzethe aggregation pathways by transition networks (25–27), whichelucidate the similarities and differences between Aβ dimer-ization steps both in solution and at the neuronal membrane.We find that the neuronal membrane reduces the dynamicsof membrane-bound Aβ42 while it also inhibits β-sheet for-mation. Here, the sugar groups of GM1 form hydrogen bondswith the peptide, thereby reducing the possibilities for otherhydrogen bonds to otherwise form. In contrast, the dimerizationin the aqueous phase is characterized by a random coil to β-sheet transition, leading to β-sheet structures similar to the onesfound in Aβ fibrils.

ResultsThe Neuronal Membrane Is in a Liquid Ordered Phase. Before weanalyze the interaction of Aβ with the neuronal membrane, wedetermine the characteristics of the latter. The mass densityprofile of each lipid and water along the membrane z axis (SIAppendix, Fig. S1) shows the distribution of the bilayer com-ponents, as well as the bilayer thickness. The positions of theheadgroups are at similar locations for POPC (PC), POPE (PE),POPS (PS), and SM. CHOL, on the other hand, is shifted towardthe hydrophobic core of the bilayer, while GM1 is farther awayfrom the bilayer center, due to the protrusion of the sugar groupsfrom the xy surface of the membrane (Fig. 1A). The headgroup-to-headgroup distance of PC, PE, and PS indicates a bilayerthickness of 4.65± 0.03 nm.

We calculated the acyl chain order parameter SCH of the C–Hbonds of all the lipid tails (SI Appendix, Fig. S2) to gain insightinto their arrangement within the membrane. Values of 0.35 to0.4 for the order parameters of carbon atoms 4 to 10 are reached,which is an increase compared to the order parameters found inother membranes (28, 29). This is due to the effects of cholesteroland sphingomyelin, which are known for their role in increasinglipid order. Notably, we find the acyl chains of GM1 and SM tobe the most ordered. We can thus conclude that the neuronalmembrane is in the liquid-ordered state, which is in agreementwith previous observations (24, 30).

GM1 Forms Ganglioside Clusters. The radial distribution function(RDF) of all possible lipid pairings was calculated to moni-tor the effect of these pairwise interactions on lipid clustering(Fig. 1 B and C and SI Appendix, Fig. S3). A distinct RDFpeak is seen at ≈0.45 nm for the self-clustering of GM1 andpronounced peaks are seen at 0.55 and 0.6 nm for the forma-tion of CHOL and SM clusters, respectively, while all otherlipids do not tend to self-associate. The self-clustering of GM1is considerably stronger than that of the other lipids. Thus, tak-ing the relatively low concentration of GM1 (4%) into account,one can conclude that GM1 has a strong tendency to self-associate that can result in its sorting. No strong clusteringbetween mixed lipid pairs is observed. Notable coassociationis seen only for SM with POPE, CHOL, and GM1. Interest-ingly, the RDF of PE–PS has a higher peak compared to that ofPE–PE and PS–PS, respectively. The dispersion of PS is under-standable given that it is negatively charged. The negative chargeof both GM1 and PS also explains why these two lipids avoidcoclustering.

To elucidate the dominant lipid–lipid interactions underlyingthe RDFs, the average numbers of hydrogen bonds (H bonds)between the different lipid pairs were evaluated. SI Appendix,Fig. S4 shows that the sorting of GM1 results from its abil-ity to build a network of H bonds via its sugar headgroups,despite its negative charge. The propensity of SM to form Hbonds with itself also gives rise to its self-clustering, whereas theminor self-clustering seen for CHOL is a result of the cholesterolcondensing effect. This effect does not result from attractivevan der Waals interactions between CHOL molecules, but froma reduced membrane perturbation energy if small cholesteroldomains are formed (31). However, such cholesterol clustersare not particularly stable, as evidenced by only a small peakin the RDF for CHOL–CHOL. The coclustering of CHOL andSM is facilitated by H bonds formed between the hydroxyl ofCHOL and the amide group of SM, which agrees with previ-ous findings (32). The RDF profile of SM–GM1 can also beexplained by H-bond formation. We conclude that H bonds playan essential role in stabilizing lipid clusters within the neuronalmembrane.

Aβ42 Dimerizes at the Neuronal Membrane and Interacts with GM1.To understand the effects of the neuronal membrane on theaggregation of Aβ42, we analyzed the 6× 2 µs of MD data inthe presence of the lipid bilayer and compared the aggregationto the 6× 2 µs of MD simulations done in the aqueous phase.We first assess whether and how the two peptides bind to andinteract with the membrane.

To follow the association between Aβ42 and the neuronalmembrane, we calculated the minimum distance of both pep-tides from the lipid bilayer surface for each of the six simulations(SI Appendix, Fig. S5). It can be seen that peptide 1 usuallyinteracts with the membrane at a closer distance than pep-tide 2 does, which can be explained by the fact that the initialstructures of five of the six simulations were selected from theinitial 2-µs simulation. This allows us to better elucidate theeffects of the membrane on the preferentially membrane-bound

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peptide as their mutual interaction time is larger than it wouldhave been if both peptides had the same interaction probabil-ity. Nonetheless, both peptides tend to be associated with themembrane as an intact dimer, since if one peptide is >0.5 nmaway from the membrane, implying that this peptide is in solu-tion, then very often this is also the case for the other peptide.Fig. 2 shows representative snapshots for the membrane associ-ation of Aβ42, including one for loose binding in Fig. 2A. Fig.2B represents the situation where peptide 1 is in close contactwith the membrane, while peptide 2 is a bit farther away. Theopposite, less prevalent situation with peptide 2 being closer isdepicted in Fig. 2C and is less common, while Fig. 2D showshow both peptides can bind tightly to the membrane. Fig. 2 fur-ther suggests that Aβ42 tends to interact with GM1 instead ofthe other lipids and that β-sheets are the dominating secondarystructure in peptide 2 but not in the more membrane-bound pep-tide 1. The analysis of the contacts between Aβ42 and the variouslipids confirms that the peptide has a high tendency to associatewith GM1, followed by PC, PE, and PS (SI Appendix, Fig. S6).Here, we emphasize that these contacts are not normalized butabsolute values. Considering that only 4% of the lipids are GM1while the phospholipids make up for more than two-thirds of themembrane, one can thus conclude that Aβ42 is highly attractedto GM1. Interestingly, almost no contacts are made withCHOL or SM.

To rationalize the driving force that controls Aβ42 interac-tion with the membrane surface, the interaction energy of eachAβ42 residue with each of the lipid components was calculatedand partitioned into its electrostatic (ECoul) and Lennard-Jones(ELJ) contributions (Fig. 3). Notably, the lipid interactions ofpeptide 1 are more favorable than those of peptide 2, agreeingwith the observation that peptide 1 interacted more strongly withthe membrane. Our results suggest that the major driving forcefor the association of the peptides to the membrane is the elec-trostatic attraction to PC, PE, and PS, especially via the highlycharged N-terminal region and residues F20 to A30. Residuesat the N terminus had the strongest interactions with the mem-brane, such as D1, E3, and D7 with PE; D1 with PC; and R5with PS. The latter interaction involves H-bond formation (SIAppendix, Fig. S7), which is enabled via the carboxylate group ofPS, whereas the primary ammonium group of PE forms H bondswith D1, E3, and D7. The tertiary ammonium group of PC, onthe other hand, does not support H-bond formation, leading to arelatively low H-bond propensity between PC (via its phosphategroup) and Aβ42. The interactions between GM1 and Aβ42 aredriven by both Coulomb and Lennard-Jones energies (Fig. 3) andare facilitated by the sugar headgroups of GM1, which protrude

from the membrane and are therefore particularly accessible toAβ42. Moreover, the interactions with GM1 derive from a con-siderable number of H bonds, which involve almost all residuesof both peptides, but particularly those of peptide 1.

No direct interaction between Aβ42 and CHOL was observed(SI Appendix, Fig. S6), due to the deeper, unexposed positionof CHOL within the membrane. Interestingly, even though SMhas the same headgroup as PC, which is also located at a similarposition along the bilayer normal, Aβ42 hardly interacted withSM. This can be understood by considering the preference of SMto form H bonds with other lipids including itself, which reducesits tendency to create H bonds with the peptide.

The Aβ42 Dimer Does Not Affect the Neuronal Membrane. To deter-mine whether the peptides affect the structure of the lipidmembrane, we calculated the lipid order parameter for the lipidsthat are within 0.5 nm of the peptide when adsorbed to themembrane (SI Appendix, Fig. S2). The results suggest no notablechange in the lipid order parameter due to the interactions withAβ42. Moreover, only a slight deviation of about ±0.1 nm wasseen in the bilayer thickness (SI Appendix, Fig. S8) at the site ofpeptide interaction. We thus conclude that the peptides interactonly with the lipid headgroups without inserting into the mem-brane, thereby preventing larger changes in the membrane orderand thickness.

Different Aggregation Pathways in Solution and at the NeuronalMembrane. To unravel differences within the aggregation path-ways, we computed transition networks (TNs) for the Aβ42dimerization both in the aqueous phase and in the presence ofthe neuronal membrane. To this end, we characterized the con-formations by assigning the aggregate state (monomer or dimer),the number of hydrophobic contacts between the peptides in adimer, and the number of residues in β-strand conformation asdescriptors. To further simplify the TNs, we grouped both thenumber of hydrophobic contacts and the number of residues inβ-strand conformation in blocks of five such that we end up withranges h1 to h12 and b1 to b6. For example, h1 and b1 standfor hydrophobic contacts and the number of residues in β-strandconformation, respectively, ranging from 1 to 5. The maximumstate h12 involves between 56 and 60 hydrophobic contacts andthe b6 state means that between 26 and 30 residues per peptideadopted a β-strand conformation.

The resulting TNs (Fig. 4) are characterized by two regions:the monomeric region (on the left side of the TNs) and thedimeric region (in the middle and the right side of the TNs),where the former evolves into the latter. These regions are

Fig. 2. Snapshots of Aβ42 interacting with the neuronal membrane. Peptide 1 and peptide 2 are shown as cartoons in red and blue, respectively, with theirtermini indicated by spheres (N, light blue; C, light red). The color coding for the membrane is the same as in Fig. 1A. Representative interaction patternsare provided: (A) both peptides being loosely attached to the bilayer surface, (B) peptide 1 being in close interaction with the membrane and peptide 2being bound to peptide 1, (C) the opposite situation to that in B, and (D) both peptides being in close contact with the membrane.

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Fig. 3. The average interaction energies of peptide 1 (Left) and peptide 2 (Right) with each lipid of the neuronal membrane. Electrostatic and Lennard-Jonesenergies are shown in blue and green, respectively. The more negative an energy is, the more attractive is the corresponding interaction.

connected by several bridging nodes, which, on average, are char-acterized by a higher amount of β-sheet (i.e., larger n in thedescriptor bn) in the case of the solution system. In both TNs,a representative bridging node is indicated by a green circle,[2, h2, b6] for the solution system and [2, h2, b2] for themembrane system, which are further augmented by a character-istic structure. In solution, there are more transitions betweenmonomers and dimers, which indicates a higher number ofassociation and dissociation events. In general, the TN for thesolution system exhibits more nodes and transitions.

A closer inspection of both TNs reveals how the two pep-tides evolve from the monomeric random coil state, which isrepresented by node [1, 0, 0] with no interpeptide hydrophobiccontacts and no residues in β-strand conformation, to dimerswith only a few hydrophobic contacts, as present in states [2, h1,bn]. Here bn ranges from b1 to b6, indicating an increase in β-strand content as the structure changes along the path throughnodes [1, 0, bn] and [2, 0, bn]. The dimers with no hydrophobiccontacts are so-called encounter complexes, where the minimaldistance between the two monomers fell below 4.5 nm, and sub-sequently form stable dimers by increasing their contact area asinterpeptide contacts form. This process stabilizes the dimer andis accompanied by an increase in β-strand content. In solution,the dimers form more interpeptide hydrophobic contacts, reach-ing states [2, h12, b6] and [2, h13, b5] wherein 50 to 70% of allAβ42 residues form a β-sheet. In the presence of the neuronalmembrane, both the hydrophobic contact area and β-sheet con-tent are reduced, with the maximal values being [2, h10, b4] and[2, h9, b5], explaining the smaller number of nodes in this TN.Some of the interpeptide contacts are replaced by peptide–lipidcontacts, which in turn inhibits β-sheet formation. This conclu-sion is confirmed by the representative structures shown in Fig.4 and those illustrating the membrane adsorption of the dimer(Fig. 2). The membrane-adsorbed dimer structures are morecompact than the dimer structures in solution, which featureextended β-sheets.

Long β-Strands in Solution and Compact Aβ42 Structures at theMembrane. To quantify the effect of both aggregation and mem-brane adsorption on the peptide secondary structure, we deter-

mined the propensity of each residue to adopt a helical con-formation, to be part of a β-sheet, or to be in a turn or bendconformation (Fig. 5A). For the dimer both in solution and onthe membrane, β-sheet formation is observed. Using the sameforce field, mostly disordered conformations were sampled forthe Aβ monomer during a 30-µs MD simulation, with an aver-age β-sheet content of about 15% (20). This rises to 36% for thedimer in solution, which indicates that dimerization causes Aβ42to undergo a disorder-to-order transition with β-sheet folding.The β-sheet content for the membrane-adsorbed dimer is 28%and thus smaller compared to that for the solvated dimer. Thisdecrease is particularly pronounced for peptide 1, which inter-acts more strongly with the membrane than peptide 2 does.Instead, peptide 1 exhibits more turns, bends, and random coilstructures, which suggests that the membrane inhibits β-sheetformation. Also, no pronounced helix formation is observedfor the membrane-bound dimer, which one might expect basedon NMR results (33) and previous simulation studies of Aβthat employed implicit membrane models (34, 35). However,a closer inspection of these studies reveals that for helices tobe present, the affected Aβ residues need to be inserted intothe hydrophobic membrane core, which did not occur here.It remains to be shown what comes first: helix formation ormembrane insertion. In solution, both peptides feature a verysimilar secondary structure pattern along their primary struc-ture. They display a particularly high propensity for a β-sheet inthe regions Q15 to F20 of the central hydrophobic core (CHC)and A30 to V40 from the C-terminal hydrophobic region. Thisexcludes the residue pair G37/G38, which has a tendency toform a turn as previously shown in simulations (36) and NMRspectroscopy (37).

The analysis of the intrapeptide contacts, derived from inter-residue distances (Fig. 6), indicates that in solution long β-hairpins between two antiparallel strands involving residues Y10to V24 and Q27 to V40 formed in both peptides. These β-hairpins are particularly stable since the β-sheet propensity ofthe strongly hydrophobic regions 18VFF20and 32IGL34 evenreaches values above 90%. In previous simulation studies, β-sheet formation upon Aβ dimerization has also been the pre-vailing finding (see table 2 of ref. 36 and references therein

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YFig. 4. The TN for Aβ42 dimerization in the aqueous phase (Top) and in the presence of the neuronal membrane (Bottom). Each node is defined by threedescriptors: oligomer size, number of interpeptide hydrophobic contacts, and number of residues in β-strand conformation. The last two descriptors aregrouped in blocks of five and are named h1 to h12 for hydrophobic contacts and b1 to b6 for the number of residues in β-strand conformation. The nodes areconnected by edges that represent transitions between the connected peptide states. The size of the nodes and the thickness of the edges are proportionalto the respective state or transition probability. They are colored based on the descriptor reflecting the number of residues in β-strand conformation (fromlight pink for no β-sheets to dark purple for the maximum amount of β-sheets in b6). For the nodes circled in green representative peptide conformationsare shown (see color code in Fig. 2).

as well as refs. 38–41). As found here, the β-sheets are pref-erentially formed between the C-terminal hydrophobic regions,followed by the involvement of the CHC. However, in most ofthese previous studies, the β-sheets are shorter and the overalldimer appearance is more compact. This likely resulted fromthe usage of older force fields, which were not optimized forIDPs and are known to provide too compact IDP conforma-tions (42). Exceptions are a coarse-grained discrete MD study

(38) and a structure-prediction study for transmembrane Aβoligomers (35) that yielded similarly extended β-sheets. Thisis confirmed by comparing the intrapeptide contacts that arepresent in the different Aβ42 dimers, as shown in SI Appendix,Fig. S9. SI Appendix, Fig. S9 further shows that the β-hairpincentered at G25/S26 coincides with the peptide regions that areinvolved in the cross–β-sheet structure found in U-shaped Aβfibrils (43, 44).

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Fig. 5. Structural characteristics of the dimer in the aqueous phase (Top) and in the presence of the neuronal membrane (Bottom). (A) Probability ofsecondary structures to form in each residue of the peptides. The bars represent the cumulative secondary structure probabilities consisting of helix (green),β-strand/bridge (magenta), and turn or bend (gray). The difference from 1.0 presents the probability of the random coil state. (B) The average orderparameter S2 of each residue and peptide.

The intrapeptide contacts present in the membrane-adsorbeddimer are more diverse and different in the two peptides. Forpeptide 2 they reveal the prevalence of two shorter hairpins,one centered at H14 and the other one at G25, and sev-eral contacts between N- and C-terminal residues. The moremembrane-adsorbed peptide 1, on the other hand, is devoid ofnoteworthy contacts involving its N-terminal residues. These arethe amino acids that preferentially interact with the membraneand are therefore not available for interresidue interactions.In the C-terminal region of peptide 2 the formation of a veryshort β-hairpin is visible. Overall, the intrapeptide contacts cor-roborate the conclusion that at the membrane Aβ42 adoptsmore compact conformations with less β-sheet than the dimerin solution.

Dimerization in Solution Is Mainly Driven via the Hydrophobic C-Terminal Region. To obtain an overview of how the two peptidesare arranged with respect to each other as dimers, we calculatedthe interpeptide distances on a per-residue basis. The resultingdistance matrices for the two dimer systems (Fig. 6) are almostsymmetric with respect to their diagonal and are characterizedby areas of high contact density along the diagonal as well as inthe upper left and lower right quadrants. Only the D23 to K28region in both peptides and in both environments does not showa noteworthy contact propensity. This is the same region of thepeptide that we assigned a turn or bend conformation (Fig. 5). Itcan thus be concluded that this bend/turn region does not formthe interpeptide interface.

For the dimer in solution, the highest contact density isobserved between the two C-terminal regions, A30 to A42, whichare the same regions where a high β-propensity was identified.Therefore, these two C-terminal regions not only are involved inintrapeptide β-sheets, but also form an interpeptide β-sheet insolution. This is confirmed when analyzing the residue–residueinteraction energies between the two peptides, which involve

Coulomb interactions deriving from backbone H bonds andLennard-Jones energies originating from interactions betweenhydrophobic residues (SI Appendix, Fig. S10). While the distancematrix does not show a clear preference for either an antiparal-lel or a parallel β-sheet between the two C-terminal regions, andboth arrangements are indeed possible (see the representativeconformations for nodes [2, h7, b4] [parallel] and [2, H12, b6][antiparallel] of the corresponding TN in Fig. 4), the interactionenergies indicate that the antiparallel arrangement is favored.This is different from Aβ fibrils where only parallel β-sheets arefound. Other preferred contacts in the dimers form between theCHC of one peptide and the C-terminal region of the other pep-tide. The fourth area with a certain, yet smaller probability ofinterpeptide contact is between the CHC regions of both pep-tides. However, these contacts are weaker than those betweenthe two C-terminal regions, as the corresponding interactionenergies are smaller in magnitude (SI Appendix, Fig. S10). Thedissection of the interaction energies further reveals that attrac-tion between the oppositely charged residues E22/D23 and K28is involved in the association process, which is in agreement withprevious findings (45).

The distance matrix of the membrane-adsorbed dimer lookssimilar to the one of the dimer in solution. However, the contactareas are more pronounced, indicating less structural diversity inthe internal arrangement of the dimers. Second, the area withoutinterpeptide contacts around residues D23 to K28 is larger. Thisapplies to peptide 1 in particular and can be explained by the con-tacts that this peptide forms with the membrane instead. Third,the order of areas with the highest contact probability is differ-ent from those of the solution system. The shortest distances inthe membrane-adsorbed dimer are observed between the CHCof peptide 1 and the C-terminal region of peptide 2, followedby the contacts between both CHC regions. However, based onthe secondary structure analysis, β-sheet formation between thetwo peptides is less likely and is largely limited to within peptide

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Fig. 6. The distance matrices illustrating intra- and interpeptide contacts between residues for the dimer in the aqueous phase (Top) and in the presence ofthe neuronal membrane (Bottom). The intrapeptide contacts within peptide 1 are shown below the main diagonal and those within peptide 2 above it. Theinterpeptide contacts are shown for peptide 1 and peptide 2 composing the dimer. The color bar on the right indicates the average intra- and interresiduedistances (in nanometers).

2. Contacts between the C-terminal region of peptide 1 and theN-terminal region of peptide 2 are also observed. As a result,the latter region exhibits an increased β-sheet propensity, whichextends up to residue Y10 (Fig. 5A). It initially was assumedthat the N-terminal region of Aβ is always disordered. However,this was later refuted, first by simulations (SI Appendix, Fig. S9)and then by cryo-electron microscopy (35, 46). Contacts betweenthe C-terminal regions are of less relevance for the membrane-adsorbed dimer due to the competition between peptide–peptideand peptide–membrane interactions. The ranking of the inter-peptide contact preferences is confirmed by the analysis of theinteraction energies (SI Appendix, Fig. S10). Unlike in solution,attraction between E22/D23 and K28 does not play a role duringthe dimerization of Aβ, which can be explained by the preferenceof K28 to associate with the membrane.

Reduced Global Motions but Increased Local Disorder in theMembrane-Adsorbed Dimer. To quantify the peptide dynamics, wecalculated the S2 order parameters to monitor the mobility ofthe N–H bond vectors of the peptide backbone along with theaverage global rotational correlation times, 〈τ〉 (Fig. 5B). Thesequantities would be directly comparable to those determined byNMR spectroscopy, which, however, are not available yet. Theglobal rotational dynamics of the Aβ42 dimer in solution occuron the low nanosecond time scale with 〈τ〉=20± 10 ns. TheS2 values reflect the different secondary structure propensitiesof the various residues. They are above ≈0.7 for the residuesin a β-conformation, while the more mobile turn region andneighboring residues ranging from E22 to A30 have S2 valuesbetween 0.5 and 0.7, and the disordered N-terminal region hasorder parameters below 0.5. The comparison to the S2 values of

the Aβ40 monomer confirm that the dimer in solution is con-siderably more folded, since for the monomer all S2 values arebelow 0.4 (47). The global rotational dynamics of the Aβ42 dimerin the presence of the neuronal membrane are by a factor of5 slower than in solution: 〈τ〉=108± 30 ns. Interestingly, theslower motion is accompanied by decreased order parameterscompared to that seen in solution; the S2 values range from0.25 to 0.55 (and below 0.25 for the N-terminal residues, simi-lar to the situation in the solution dimer). The overall reductionin S2 for the membrane-adsorbed dimer implies that the pep-tides are generally less folded than they are in solution, whichagrees with the observed reduction in β-sheet and increase inrandom coil. Thus, a picture emerges where on the one hand theoverall peptide dynamics are reduced due to the adsorption onthe membrane, while at the same time the interactions with themembrane reduce the local peptide order as reflected by the S2

values.

DiscussionIn the present study, all-atom MD simulations on the microsec-ond time scale have been performed to elucidate the mechanismof Aβ42 dimerization in pure water and in the presence of aneuronal membrane. The consideration of a neuronal mem-brane consisting of six components (PC, PE, PS, CHOL, SM,and GM1) is a major step forward compared to previous sim-ulation studies on Aβ–membrane interactions, which includedthree lipid types or fewer. Dimerization was observed in theaqueous phase as well as at the neuronal membrane. How-ever, the resulting dimer structures showed significant differ-ences. Our simulations of Aβ42 dimerization in solution revealeda coil-to-β transition that is the first step along the amyloid

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aggregation pathway. The dimer conformations sampled in solu-tion bear certain similarities to the β-sheets found in the U-shaped Aβ42 amyloid fibrils. To our knowledge, a dimer struc-ture with such a high β-sheet content and overall order has neverbeen reported from all-atom MD simulations where the aggrega-tion of Aβ progresses from disordered monomers into oligomers.We conclude that only the MD sampling of several microsec-onds and the use of a force field well suited to Aβ allow therandom coil to β-sheet transition to be observed in a simulation(22). Thus, with these simulations we finally shed light on thestructural transitions that might lead to nuclei enabling amyloidformation. Our future simulations will test whether the dimersthat formed in solution here are indeed on pathway towardamyloid fibrils.

On the neuronal membrane, the dimer conformations are gen-erally less ordered than in solution. The dimerization took placeon the membrane, with one of the two peptides being preferen-tially adsorbed to the membrane and the other one associatingwith the already membrane-attached peptide without notewor-thy interacting with the membrane itself. The directly adsorbedpeptide in particular has a higher amount of random coil and lessβ-sheet. The membrane adsorption is mainly driven by electro-static interactions between the charged N-terminal residues ofAβ and the headgroups of PC, PE, and PS, in addition to hydro-gen bonding between the sugar moieties of the GM1 lipids andAβ42 residues across its whole primary structure. GM1 is foundto form clusters within the neuronal membrane, which are thepreferable site for Aβ to bind to the membrane surface. Thisis in line with experimental results that revealed GM1 as partof a neuronal membrane to be the main interaction partner ofAβ, whereas less binding was seen for SM and also PC (48).No insertion of the peptides into the hydrophobic region of themembrane was observed in our simulations. Instead, the interac-tions with the membrane stiffened both peptides, restricting theirconformational diversity compared to the Aβ42 dimer simulatedin the aqueous phase. Not only did the transition networks reveala reduction in the number of conformational states, but also thecorrelation times of the N–H bond vector motions indicated animpaired peptide motion. However, while adsorption was foundto have profound effects on the Aβ42 dimer, the membrane wasonly marginally affected.

Our observations are in agreement with a large and diverse setof experimental results. Of special note is a study that analyzedthe effects of glucose on Aβ42 aggregation (49). In this study,Kedia et al. (49) found that Aβ42 forms low-molecular-weightoligomers in the presence of sugars and that these oligomersdo not adopt a β-sheet structure. This agrees with our obser-vation that Aβ42 dimers that preferentially interact with theglycans of GM1 form fewer β-sheets than Aβ42 dimers thatform in solution do. Moreover, another study revealed thatAβ oligomers that are present in the brain interstitial fluidare sequestered from that fluid by strongly binding to GM1,which also prevented the further aggregation of Aβ (48). Weare aware of studies by Ikeda et al. (50) and Matsuzaki (51)that concluded that GM1 exhibits a strong Abeta fibril seed-ing potential following the formation of β-sheet–rich oligomerson GM1 clusters. However, these clusters are much larger thanthose formed in our simulations, as Ikeda et al. (50) and Mat-suzaki (51) employed ganglioside-rich (>20 mol% vs. the 4mol% used in our study) membranes, where GM1 forms an inter-connected network of micrometer size yielding glycan platformsin liquid-ordered membranes. As elaborated by Hof and cowork-ers (52), the scenarios for membranes with high and low GM1contents are not necessarily contradicting each other but rathercomplementary.

Another finding by the study of Kedia et al. (49) was thatthe unstructured Aβ42 oligomers that formed in the presenceof glucose are able to interact with membrane bilayers. Their

diffusion decreased by a factor of about 4 upon membraneadsorption, which agrees nicely with our observation that mem-brane interactions reduce the dynamics of the dimer. Moreover,no incorporation of the unstructured Aβ42 oligomers into themembrane was recorded (49), which also concurs with our find-ings. We conclude that, if a β-sheet structure should be requiredfor membrane insertion of Aβ aggregates to occur, GM1 inthe neuronal membrane has a neuroprotective effect as it couldbreak the β-sheet structure in the Aβ dimer. This finding wouldbe in agreement with the neuroprotective and neurogenerativeeffects reported for GM1 (53–55) and the conclusion that theneurotoxic activity of amyloid oligomers increases with their β-sheet content (8). On the other hand, Selkoe and coworkers (48)found that even though GM1 sequesters Aβ from the brain inter-stitial fluid, thereby inhibiting the aggregation of Aβ, the bindingof the peptide to GM1 alone mediates neurotoxic effects. Thisonce more highlights that the interplay between Aβ, its aggrega-tion, and the neuronal membrane is far from trivial and despitethe wealth of already published studies on that matter, furtherstudies are needed to fully solve this puzzle.

Materials and MethodsSetup of the Simulated Systems. The systems modeled are composed of twoAβ42 peptides, which were simulated in the aqueous phase and in the pres-ence of the neuronal lipid membrane. The initial Aβ42 structures were takenfrom the most populated clusters from a preceding 3-µs MD simulation ofmonomeric Aβ42 in solution. The neuronal membrane model composed of152 PC, 96 PE, 20 PS, 80 CHOL, 36 SM, and 16 GM1 molecules was generatedas symmetric lipid bilayer using the CHARMM-GUI interface (56).

The simulated membrane system also contained water layers above theupper and beneath the lower membrane leaflet, using the three-site trans-ferable intermolecular potential (TIP3P) for modeling the water molecules,with sodium and chloride ions added at the physiological concentration of150 mM. The two Aβ42 peptides were placed in the upper water layer ata distance of ≈2 nm from the equilibrated lipid bilayer surface and at adistance of>1 nm between the closest atoms from the two peptides. All dis-tances from the peptides to any of the simulation box edges were at least 1.2nm to avoid interactions between the peptides and their periodic images.The total number of atoms in the modeled membrane system was≈160,000atoms and the box size was about 9.6× 9.6× 13.6 nm3. The setup of thesystem in the aqueous phase was similar, but without a lipid bilayer, result-ing in a system size of about 9.2× 9.2× 6.5 nm3, and contained ≈54,760atoms. This amounts to peptide concentrations of 4 and 6 mM, respectively.This is two to three orders of magnitude higher than the concentrationsused in corresponding in vitro experiments. However, it is beyond our com-putational capabilities to model µM peptide concentrations at the atomisticlevel. Moreover, simulations at such low concentrations would most of thetime simulate only the diffusion of monomeric peptides (57). We there-fore aim to model the oligomerization of Aβ in a stepwise fashion (57, 58),starting here with simulations of dimers.

MD Simulation Conditions. The all-atom MD simulations were performedusing GROMACS/2018.2 (59) along with the CHARMM36m force field forAβ42 (60) and Charmm36 for the lipids (61). Each system was first energyminimized using the steepest-descent algorithm to remove atomic clashes.This was followed by equilibration in the canonical ensemble where a tem-perature of 310 K was regulated with the velocity-rescale thermostat (62).Next, the system was equilibrated under isobaric–isothermic conditions toobtain a pressure of 1.0 bar, where the pressure was regulated using asemi-isotropic Parrinello–Rahman pressure coupling scheme (63). Periodicboundary conditions were set in all directions. Both the van der Waalsand Coulomb force cutoffs were set to 1.2 nm in real space. The parti-cle mesh Ewald (PME) method was applied for calculating the electrostaticinteractions. Before we studied the interaction of Aβ42 with the neuronalmembrane, we equilibrated the membrane without peptides being presentfor 1 µs. For Aβ42 dimer systems, an initial simulation was run for 2 µs,from which different snapshots were randomly selected and used as start-ing structures for the next 5× 2-µs simulations. For the subsequent analysis,we combined the data from the six independent simulations and derived theresults presented in this study.

Analysis of the Lipid Bilayer Properties. For the determination of the orderparameter of the lipid acyl chains, SCH, one uses the C–H bond vectors

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present in the lipid tails and calculates the orientation of these vectors withrespect to the bilayer normal (the z axis) using

SCH =〈3cos2 θ− 1〉

2, [1]

where θ is the angle between the C–H bond vector and the bilayernormal. The angular brackets indicate the ensemble average. This calcu-lation was accomplished with a Python script available at https://github.com/NMRLipids/MATCH (64).

The mass density profiles along the bilayer normal were calculated usingthe “gmx density” tool. The distance between the peaks of the total densitygives an estimate of the bilayer thickness. Furthermore, the bilayer thicknesswas calculated as the z-position difference between the P atoms of the lipidheadgroups in the upper and lower leaflets using the “gmx distance” tool.The RDF provides information about the probability of finding a particleat a certain distance from another particle. We calculated the radial distri-bution functions of different lipid pairs in two dimensions (the xy plane)using the “gmx rdf” tool. The hydrogen bonds between different lipidpairs were determined using “gmx hbond.” A hydrogen bond was recordedwhen the angle between the donor and acceptor bonded hydrogen wasbetween 150 and 180◦ and the distance between the two atoms waswithin 0.35 nm.

Analysis of Aβ42 Properties. The secondary structure of each Aβ42 residuewas determined using the “define secondary structure program” (DSSP) (65)invoked via the GROMACS tool “do dssp.” To facilitate a clear representa-tion, the data of similar secondary structures are grouped together: β-strandand β-bridge are combined as β-sheet and β-turn and bend as turn/bend;and the helix includes α, π, and 310-helices.

For the calculation of the S2 order parameter we used the MOPS2 (Molec-ular Order Parameter S2) software developed in ref. 66 to calculate S2 fromthe N–H bond vector autocorrelation function. To facilitate the calculation,each trajectory was divided into subtrajectories of tsub = 100 ns length. Foreach of the subtrajectories the S2 values and the rotational correlationtimes, τ , were calculated and subsequently averaged over all subtrajecto-ries. The rotational correlation times were further averaged over all residuesand both peptides, denoted as 〈τ〉, whereas S2 is provided per residue andpeptide. Since 〈τ〉 for the membrane system is in the same range as tsub, wechecked on the convergence for the S2 calculation in this case (SI Appendix,Fig. S11).

Transition Networks. For the generation of the TNs to characterize theassembly of peptides into dimers we used the ATRANET (Automated Transi-tion Network) software (https://github.com/strodel-group/ATRANET) (27). Itdefines the oligomerization state by a number of descriptors, depending onthe properties of interest. In our case, three descriptors are used: The firstone is the oligomer size, which can be 1 in the case of monomer or 2 in

the case of a dimer. To define a dimer, the minimum distance between anyatom of peptide 1 and any atom of peptide 2 along with the requirementof this distance to be within 0.45 nm was used. The second descriptor, thenumber of hydrophobic contacts between both peptides, counts the possi-ble interpeptide atom pairs formed between the hydrophobic amino acidsof Aβ42 that are within a certain cutoff (also 0.45 nm). The third descrip-tor is the number of residues in β-strand conformation, which is evaluatedusing DSSP and averaged over both peptides. Feeding these descriptors toATRANET leads to a transition matrix that can be visualized using Gephi (67).Snapshots of the representative structures from the transition network wererendered using the visual molecular dynamics (VMD) program (68).

Calculation of Aβ42–Bilayer Interactions. The peptide–lipid interactionswere analyzed by calculating the interaction energy between each Aβ42residue and the headgroup of each lipid component using “gmx energy.”The “gmx mindist” program was employed to determine the number ofcontacts between each Aβ42 residue and each lipid component in the neu-ronal membrane. A contact was recorded when the distance between anytwo nonhydrogen atoms from a residue and a lipid was within 0.5 nm.The H-bond propensity was determined by the number of times an H bondwas formed between hydrogen bond donating and accepting atoms in lipidpairs.

Data Availability. The MD trajectories and the analysis scripts are avail-able at Mendeley Data, https://data.mendeley.com/datasets/92mkp4pk86.All data resulting from the analysis of this raw data is shown in the maintext or SI Appendix.

ACKNOWLEDGMENTS. H.F., M.K., A.S.-A., and B.S. acknowledge funding forthis project from the Palestinian-German Science Bridge financed by theGerman Federal Ministry of Education and Research. B.S. received fund-ing for this project from the Deutsche Forschungsgemeinschaft (GermanResearch Foundation, https://www.dfg.de/) through Grant 267205415 (CRC1208, Project A07). M.C.O. received funding for this project from the Euro-pean Union’s Horizon 2020 research and innovation programme under theMarie Skłodowska-Curie grant and it is cofinanced by the South MoravianRegion under Grant 665860. This article reflects only the authors’ viewand the European Union is not responsible for any use that may be madeof the information it contains. This research was supported by the Euro-pean Union and the Hungarian State, cofinanced by the European RegionalDevelopment Fund in the framework of the GINOP-2.3.4-15-2016-00004project, aimed to promote the cooperation between the higher educa-tion and the industry. M.C.O. and B.S. gratefully acknowledge the GaussCentre for Supercomputing (GCS) e.V. (www.gauss-centre.eu) for fund-ing this project by providing computing time on the GCS SupercomputerSuperMUC-NG at Leibniz Supercomputing Centre (https://www.lrz.de/).H.F., M.K., and B.S. gratefully acknowledge the computing time grantedthrough Julich Aachen Research Alliance - High Performance Comput-ing (Projects JICS6C and AMYLOID-MSM) on the supercomputer Jureca atForschungszentrum Julich.

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